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      SUBROUTINE <a name="SORMBR.1"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a>( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
     $                   LDC, WORK, LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          SIDE, TRANS, VECT
      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
     $                   WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If VECT = 'Q', <a name="SORMBR.20"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a> overwrites the general real M-by-N matrix C
</span><span class="comment">*</span><span class="comment">  with
</span><span class="comment">*</span><span class="comment">                  SIDE = 'L'     SIDE = 'R'
</span><span class="comment">*</span><span class="comment">  TRANS = 'N':      Q * C          C * Q
</span><span class="comment">*</span><span class="comment">  TRANS = 'T':      Q**T * C       C * Q**T
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If VECT = 'P', <a name="SORMBR.26"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a> overwrites the general real M-by-N matrix C
</span><span class="comment">*</span><span class="comment">  with
</span><span class="comment">*</span><span class="comment">                  SIDE = 'L'     SIDE = 'R'
</span><span class="comment">*</span><span class="comment">  TRANS = 'N':      P * C          C * P
</span><span class="comment">*</span><span class="comment">  TRANS = 'T':      P**T * C       C * P**T
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Here Q and P**T are the orthogonal matrices determined by <a name="SGEBRD.32"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a> when
</span><span class="comment">*</span><span class="comment">  reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
</span><span class="comment">*</span><span class="comment">  P**T are defined as products of elementary reflectors H(i) and G(i)
</span><span class="comment">*</span><span class="comment">  respectively.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
</span><span class="comment">*</span><span class="comment">  order of the orthogonal matrix Q or P**T that is applied.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
</span><span class="comment">*</span><span class="comment">  if nq &gt;= k, Q = H(1) H(2) . . . H(k);
</span><span class="comment">*</span><span class="comment">  if nq &lt; k, Q = H(1) H(2) . . . H(nq-1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
</span><span class="comment">*</span><span class="comment">  if k &lt; nq, P = G(1) G(2) . . . G(k);
</span><span class="comment">*</span><span class="comment">  if k &gt;= nq, P = G(1) G(2) . . . G(nq-1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VECT    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'Q': apply Q or Q**T;
</span><span class="comment">*</span><span class="comment">          = 'P': apply P or P**T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SIDE    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'L': apply Q, Q**T, P or P**T from the Left;
</span><span class="comment">*</span><span class="comment">          = 'R': apply Q, Q**T, P or P**T from the Right.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TRANS   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  No transpose, apply Q  or P;
</span><span class="comment">*</span><span class="comment">          = 'T':  Transpose, apply Q**T or P**T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix C. M &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns of the matrix C. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  K       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          If VECT = 'Q', the number of columns in the original
</span><span class="comment">*</span><span class="comment">          matrix reduced by <a name="SGEBRD.71"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a>.
</span><span class="comment">*</span><span class="comment">          If VECT = 'P', the number of rows in the original
</span><span class="comment">*</span><span class="comment">          matrix reduced by <a name="SGEBRD.73"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a>.
</span><span class="comment">*</span><span class="comment">          K &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input) REAL array, dimension
</span><span class="comment">*</span><span class="comment">                                (LDA,min(nq,K)) if VECT = 'Q'
</span><span class="comment">*</span><span class="comment">                                (LDA,nq)        if VECT = 'P'
</span><span class="comment">*</span><span class="comment">          The vectors which define the elementary reflectors H(i) and
</span><span class="comment">*</span><span class="comment">          G(i), whose products determine the matrices Q and P, as
</span><span class="comment">*</span><span class="comment">          returned by <a name="SGEBRD.81"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.
</span><span class="comment">*</span><span class="comment">          If VECT = 'Q', LDA &gt;= max(1,nq);
</span><span class="comment">*</span><span class="comment">          if VECT = 'P', LDA &gt;= max(1,min(nq,K)).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (input) REAL array, dimension (min(nq,K))
</span><span class="comment">*</span><span class="comment">          TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment">          reflector H(i) or G(i) which determines Q or P, as returned
</span><span class="comment">*</span><span class="comment">          by <a name="SGEBRD.91"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a> in the array argument TAUQ or TAUP.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C       (input/output) REAL array, dimension (LDC,N)
</span><span class="comment">*</span><span class="comment">          On entry, the M-by-N matrix C.
</span><span class="comment">*</span><span class="comment">          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
</span><span class="comment">*</span><span class="comment">          or P*C or P**T*C or C*P or C*P**T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDC     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array C. LDC &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', LWORK &gt;= max(1,N);
</span><span class="comment">*</span><span class="comment">          if SIDE = 'R', LWORK &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">          For optimum performance LWORK &gt;= N*NB if SIDE = 'L', and
</span><span class="comment">*</span><span class="comment">          LWORK &gt;= M*NB if SIDE = 'R', where NB is the optimal
</span><span class="comment">*</span><span class="comment">          blocksize.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.115"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
      CHARACTER          TRANST
      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.129"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.130"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
      EXTERNAL           <a name="ILAENV.131"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>, <a name="LSAME.131"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SORMLQ.134"></a><a href="sormlq.f.html#SORMLQ.1">SORMLQ</a>, <a name="SORMQR.134"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>, <a name="XERBLA.134"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      APPLYQ = <a name="LSAME.144"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'Q'</span> )
      LEFT = <a name="LSAME.145"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'L'</span> )
      NOTRAN = <a name="LSAME.146"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> )
      LQUERY = ( LWORK.EQ.-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     NQ is the order of Q or P and NW is the minimum dimension of WORK
</span><span class="comment">*</span><span class="comment">
</span>      IF( LEFT ) THEN
         NQ = M
         NW = N
      ELSE
         NQ = N
         NW = M
      END IF
      IF( .NOT.APPLYQ .AND. .NOT.<a name="LSAME.158"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'P'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.LEFT .AND. .NOT.<a name="LSAME.160"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'R'</span> ) ) THEN
         INFO = -2
      ELSE IF( .NOT.NOTRAN .AND. .NOT.<a name="LSAME.162"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'T'</span> ) ) THEN
         INFO = -3
      ELSE IF( M.LT.0 ) THEN
         INFO = -4
      ELSE IF( N.LT.0 ) THEN
         INFO = -5
      ELSE IF( K.LT.0 ) THEN
         INFO = -6
      ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
     $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
     $          THEN
         INFO = -8
      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
         INFO = -11
      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
         INFO = -13
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         IF( APPLYQ ) THEN
            IF( LEFT ) THEN
               NB = <a name="ILAENV.183"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="SORMQR.183"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>'</span>, SIDE // TRANS, M-1, N, M-1,
     $                      -1 )
            ELSE
               NB = <a name="ILAENV.186"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="SORMQR.186"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>'</span>, SIDE // TRANS, M, N-1, N-1,
     $                      -1 )
            END IF   
         ELSE
            IF( LEFT ) THEN
               NB = <a name="ILAENV.191"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="SORMLQ.191"></a><a href="sormlq.f.html#SORMLQ.1">SORMLQ</a>'</span>, SIDE // TRANS, M-1, N, M-1,
     $                      -1 ) 
            ELSE
               NB = <a name="ILAENV.194"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="SORMLQ.194"></a><a href="sormlq.f.html#SORMLQ.1">SORMLQ</a>'</span>, SIDE // TRANS, M, N-1, N-1,
     $                      -1 )
            END IF
         END IF
         LWKOPT = MAX( 1, NW )*NB
         WORK( 1 ) = LWKOPT 
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.203"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SORMBR.203"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a>'</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      WORK( 1 ) = 1
      IF( M.EQ.0 .OR. N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( APPLYQ ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Apply Q
</span><span class="comment">*</span><span class="comment">
</span>         IF( NQ.GE.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Q was determined by a call to <a name="SGEBRD.221"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a> with nq &gt;= k
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="SORMQR.223"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, LWORK, IINFO )
         ELSE IF( NQ.GT.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Q was determined by a call to <a name="SGEBRD.227"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a> with nq &lt; k
</span><span class="comment">*</span><span class="comment">
</span>            IF( LEFT ) THEN
               MI = M - 1
               NI = N
               I1 = 2
               I2 = 1
            ELSE
               MI = M
               NI = N - 1
               I1 = 1
               I2 = 2
            END IF
            CALL <a name="SORMQR.240"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
     $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
         END IF
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Apply P
</span><span class="comment">*</span><span class="comment">
</span>         IF( NOTRAN ) THEN
            TRANST = <span class="string">'T'</span>
         ELSE
            TRANST = <span class="string">'N'</span>
         END IF
         IF( NQ.GT.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           P was determined by a call to <a name="SGEBRD.254"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a> with nq &gt; k
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="SORMLQ.256"></a><a href="sormlq.f.html#SORMLQ.1">SORMLQ</a>( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, LWORK, IINFO )
         ELSE IF( NQ.GT.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           P was determined by a call to <a name="SGEBRD.260"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a> with nq &lt;= k
</span><span class="comment">*</span><span class="comment">
</span>            IF( LEFT ) THEN
               MI = M - 1
               NI = N
               I1 = 2
               I2 = 1
            ELSE
               MI = M
               NI = N - 1
               I1 = 1
               I2 = 2
            END IF
            CALL <a name="SORMLQ.273"></a><a href="sormlq.f.html#SORMLQ.1">SORMLQ</a>( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
     $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
         END IF
      END IF
      WORK( 1 ) = LWKOPT
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SORMBR.280"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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